1 Matrix Multiplication Problems
1.1 Basic Algorithms and Notation
1.2 Exploiting Structure
1.3 Block Matrices and Algorithms
1.4 Vectorization and Re-Use Issues
2 Matrix Analysis
2.1 Basic Ideas from Linear Algebra
2.2 Vector Norms
2.3 Matrix Norms
2.4 Finite Precision Matrix Computations
2.5 Orthogonality and the SVD
2.6 Projections and the CS Decomposition
2.7 The Sensitivity of Square Linear Systems
3 General Linear Systems
3.1 Triangular Systems
3.2 The LU Factorization
3.3 Roundoff Analysis of Gaussian Elimination
3.4 Pivoting
3.5 Improving and Estimating Accuracy
4 Special Linear Systems
4.1 The LDMT and LDLT Factorizations
4.2 Positive Definite Systems
4.3 Banded Systems
4.4 Symmetric Indefinite Systems
4.5 Block Systems
4.6 Vandermonde Systems and the FFT
4.7 Toeplitz and Related Systems
5 Orthogonalization and Least Squares
5.1 Householder and Givens Matrices
5.2 The QR Factorization
5.3 The Full Rank LS Problem
5.4 Other Orthogonal Factorizations
5.5 The Rank Deficient LS Problem
5.6 Weighting and Iterative Improvement
5.7 Square and Underdetermined Systems
6 Parallel Matrix Computations
6.1 Basic Concepts
6.2 Matrix Multiplication
6.3 Factorizations
7 The Unsymmetric Eigenvalue Problem
8 The Symmetric Eigenvalue Problem
9 Lanczos Methods
10 Iterative Methods for Linear Systems
11 Functions of Matrices
12 Special Topics
Index